IJMPCERO  Vol.4 No.2 , May 2015
Biological Dose Estimation Model for Proton Beam Therapy
Purpose: The recommended value for the relative biological effectiveness (RBE) of proton beams is currently assumed to be 1.1. However, there is increasing evidence that RBE increases towards the end of proton beam range that may increase the biological effect of proton beam in the distal regions of the dose deposition. Methods: A computational approach is presented for estimating the biological effect of the proton beam. It includes a method for calculating the dose averaged linear energy transfer (LET) along the measured Bragg peak and published LET to RBE conversion routine. To validate the proposed method, we have performed Monte Carlo simulations of the pristine Bragg peak at various beam energies and compared the analysis with the simulated results. A good agreement within 5% is observed between the LET analysis of the modeled Bragg peaks and Monte Carlo simulations. Results: Applying the method to the set of Bragg peaks measured at a proton therapy facility we have estimated LET and RBE values along each Bragg peak. Combining the individual RBE-weighted Bragg peaks with known energy modulation weights we have calculated the RBE-weighted dose in the modulated proton beam. The proposed computational method provides a tool for calculating dose averaged LET along the measured Bragg peak. Conclusions: Combined with a model to convert LET into RBE, this method enables calculation of RBE-weighted dose both in pristine Bragg peak and in modulated beam in proton therapy.
Cite this paper: Anferov, V. , Das, I. (2015) Biological Dose Estimation Model for Proton Beam Therapy. International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, 4, 149-161. doi: 10.4236/ijmpcero.2015.42019.

[1]   Sheets, N.C., Goldin, G.H., Meyer, A.-M., Wu, Y., Chang, Y., Stuürmer, T., Holmes, J.A., Reeve, B.B., Godley, P.A., Carpenter, W.R. and Chen, R.C. (2012) Intensity-Modulated Radiation Therapy, Proton Therapy, or Conformal Radiation Therapy and Morbidity and Disease Control in Localized Prostate Cancer. JAMA, 307, 1611-1620.

[2]   St. Clair, W.H., Adams, J.A., Bues, M., Fullerton, B.C., La Shell, S., Kooy, H.M., Loeffler, J.S. and Tarbell, N.J. (2004) Advantage of Protons Compared to Conventional x-Ray or Imrt in the Treatment of a Pediatric Patient with Medulloblastoma. International Journal of Radiation Oncology Biology Physics, 58, 727-734.

[3]   Brown, A.P., Barney, C.L., Grosshans, D.R., McAleer, M.F., de Groot, J.F., Puduvalli, V.K., Tucker, S.L., Crawford, C.N., Khan, M., Khatua, S., Gilbert, M.R., Brown, P.D. and Mahajan, A. (2013) Proton Beam Craniospinal Irradiation Reduces Acute Toxicity for Adults with Medulloblastoma. International Journal of Radiation Oncology Biology Physics, 86, 277-284.

[4]   Moeller, B.J., Chintagumpala, M., Philip, J.J., Grosshans, D.R., McAleer, M.F., Woo, S.Y., Gidley, P.W., Vats, T.S. and Mahajan, A. (2011) Low Early Ototoxicity Rates for Pediatric Medulloblastoma Patients Treated with Proton Radiotherapy. Radiation Oncology, 6, 58.

[5]   Blakely, E.A. and Chang, P.Y. (2009) Biology of Charged Particles. Cancer Journal, 15, 271-284.

[6]   ICRU Report 78 (2007) Prescribing, Recording, and Reporting Proton Beam Therapy. International Commission on Radiation Units and Measurements.

[7]   IAEA TRS 461 (2008) Relative Biological Effectiveness in Ion Beam Therapy. International Atomic Energy Agency.

[8]   Bashkirov, V. and Schulte, R.W. (2002) Dosimetry System for the Irradiation of Thin Biological Samples with Therapeutic Proton Beams. Physics in Medicine and Biology, 47, 409-420.

[9]   Britten, R.A., Nazaryan, V., Davis, L.K., Klein, S.B., Nichiporov, D., Mendonca, M.S., Wolanski, M., Nie, X., George, J. and Keppel, C. (2013) Variations in the Rbe for Cell Killing along the Depth-Dose Profile of a Modulated Proton Therapy Beam. Radiation Research, 179, 21-28.

[10]   Gueulette, J., Blattmann, H., Pedroni, E., Coray, A., Decoster, B., Mahy, P., Wambersie, A. and Goitein, G. (2005) Relative Biologic Effectiveness Determination in Mouse Intestine for Scanning Proton Beam at Paul Scherrer Institute, Switzerland. Influence of Motion. International Journal of Radiation Oncology Biology Physics, 62, 838-845.

[11]   Gueulette, J., Bohm, L., De Coster, B.M., Vynckier, S., Octave-Prignot, M., Schreuder, A.N., Symons, J.E., Jones, D.T., Wambersie, A. and Scalliet, P. (1997) RBE Variation as a Function of Depth in the 200-MeV Proton Beam Produced at the National Accelerator Centre in Faure (South Africa). Radiotherapy and Oncology, 42, 303-309.

[12]   Kagawa, K., Murakami, M., Hishikawa, Y., Abe, M., Akagi, T., Yanou, T., Kagiya, G., Furusawa, Y., Ando, K., Nojima, K., Aoki, M. and Kanai, T. (2002) Preclinical Biological Assessment of Proton and Carbon Ion Beams at Hyogo ion Beam Medical Center. International Journal of Radiation Oncology Biology Physics, 54, 928-938.

[13]   Raju, M.R., Amols, H.I., Bain, E., Carpenter, S.G., Cox, R.A. and Robertson, J.B. (1978) A Heavy Particle Comparative Study. Part III: OER and RBE. British Journal of Radiology, 51, 712-719.

[14]   Giantsoudi, D., Grassberger, C., Craft, D., Niemierko, A., Trofimov, A. and Paganetti, H. (2013) Linear Energy Transfer-Guided Optimization in Intensity Modulated Proton Therapy: Feasibility Study and Clinical Potential. International Journal of Radiation Oncology Biology Physics, 87, 216-222.

[15]   Carabe, A., Espana, S., Grassberger, C. and Paganetti, H. (2013) Clinical Consequences of Relative Biological Effectiveness Variations in Proton Radiotherapy of the Prostate, Brain and Liver. Physics in Medicine and Biology, 58, 2103-2117.

[16]   Pehlivan, B., Ares, C., Lomax, A.J., Stadelmann, O., Goitein, G., Timmermann, B., Schneider, R.A. and Hug, E.B. (2012) Temporal Lobe Toxicity Analysis after Proton Radiation Therapy for Skull Base Tumors. International Journal of Radiation Oncology Biology Physics, 83, 1432-1440.

[17]   Tilly, N., Johansson, J., Isacsson, U., Medin, J., Blomquist, E., Grusell, E. and Glimelius, B. (2005) The Influence of RBE Variations in a Clinical Proton Treatment Plan for a Hypopharynx Cancer. Physics in Medicine and Biology, 50, 2765-2777.

[18]   Jones, B., Wilson, P., Nagano, A., Fenwick, J. and McKenna, G. (2012) Dilemmas Concerning Dose Distribution and the Influence of Relative Biological Effect in Proton Beam Therapy of Medulloblastoma. British Journal of Radiology, 85, e912-e918.

[19]   Grassberger, C. and Paganetti, H. (2011) Elevated Let Components in Clinical Proton Beams. Physics in Medicine and Biology, 56, 6677-6691.

[20]   Grassberger, C., Trofimov, A., Lomax, A. and Paganetti, H. (2011) Variations in Linear Energy Transfer within Clinical Proton Therapy Fields and the Potential for Biological Treatment Planning. International Journal of Radiation Oncology Biology Physics, 80, 1559-1566.

[21]   Belli, M., Campa, A. and Ermolli, I. (1997) A Semi-Empirical Approach to the Evaluation of the Relative Biological Effectiveness of Therapeutic Proton Beams: The Methodological Framework. Radiation Research, 148, 592-598.

[22]   Wilkens, J.J. and Oelfke, U. (2004) A Phenomenological Model for the Relative Biological Effectiveness in Therapeutic Proton Beams. Physics in Medicine and Biology, 49, 2811-2825.

[23]   Neary, G.J. (1965) The Relation between the Exponent of Dose Response for Chromosome Aberrations and the Relative Contribution of “Two-Track” and “One-Track” Processes. Mutation Research, 2, 242-246.

[24]   Paganetti, H. and Goitein, M. (2000) Radiobiological Significance of Beamline Dependent Proton Energy Distributions in a Spread-Out Bragg Peak. Medical Physics, 27, 1119-1126.

[25]   His, W.C., Moyers, M.F., Nichiporov, D., Anferov, V., Wolanski, M., Allgower, C.E., Farr, J.B., Mascia, A.E. and Schreuder, A.N. (2009) Energy Spectrum Control for Modulated Proton Beams. Medical Physics, 36, 2297-2308.

[26]   Frese, M.C., Yu, V.K., Stewart, R.D. and Carlson, D.J. (2012) A Mechanism-Based Approach to Predict the Relative Biological Effectiveness of Protons and Carbon Ions in Radiation Therapy. International Journal of Radiation Oncology Biology Physics, 83, 442-450.

[27]   Kantemiris, I., Karaiskos, P., Papagiannis, P. and Angelopoulos, A. (2011) Dose and Dose Averaged LET Comparison of 1H, 4He, 6Li, 8Be, 10B, 12C, 14N, and 16O Ion Beams Forming a Spread-Out Bragg Peak. Medical Physics, 38, 6585-6591.

[28]   Nikjoo, H., Uehara, S., Wilson, W.E., Hoshi, M. and Goodhead, D.T. (1998) Track Structure in Radiation Biology: Theory and Applications. International Journal of Radiation Biology, 73, 355-364.

[29]   Ottolenghi, A., Merzagora, M. and Paretzke, H.G. (1997) DNA Complex Lesions Induced by Protons and α-Particles: Track Structure Characteristics Determining Linear Energy Transfer and Particle Type Dependence. Radiation and Environmental Biophysics, 36, 97-103.

[30]   Zaider, M., Brenner, D.J. and Wilson, W.E. (1983) The Applications of Tack Calculations to Radiobiology I. Monte Carlo Simulation of Proton Tracks. Radiation Research, 95, 231-247.

[31]   Barendsen, G.W. (1994) RBE-LET Relationships for Different Types of Lethal Radiation Damage in Mammalian Cells: Comparison with DNA Dsb and an Interpretation of Differences in Radiosensitivity. International Journal of Radiation Biology, 66, 433-436.

[32]   Belli, M., Cera, F., Cherubini, R., Dalla Vecchia, M., Haque, A.M., Ianzini, F., Moschini, G., Sapora, O., Simone, G., Tabocchini, M.A. and Tiveron, P. (1998) RBE-LET Relationships for Cell Inactivation and Mutation Induced by Low Energy Protons in v79 Cells: Further Results at the LNL Facility. International Journal of Radiation Biology, 74, 501-509.

[33]   ICRU (1993) ICRU Report 49, Stopping Powers and Ranges for Protons and Alpha Particles. International Commission on Radiation Units and Measurements.

[34]   Paganetti, H., Niemierko, A., Ancukiewicz, M., Gerweck, L.E., Goitein, M., Loeffler, J.S. and Suit, H.D. (2002) Relative Biological Effectiveness (RBE) Values for Proton Beam Therapy. International Journal of Radiation Oncology Biology Physics, 53, 407-421.

[35]   Janni, J.F. (1966) Calculations of Energy Loss, Range, Pathlength, Straggling, Multiple Scattering, and the Probability of Inelastic Nuclear Collisions for 0.1- to 1000-MeV Protons. Air Force Weapons Laboratory, Technical Report No. AFWL-TR-65-150.

[36]   Gomà, C., Andreo, P. and Sempau, J. (2013) Spencer-Attix Water/Medium Stopping-Power Ratios for the Dosimetry of Proton Pencil Beams. Physics in Medicine and Biology, 58, 2509-2522.

[37]   Pelowitz, D.B., Hendricks, J.S., Durkee, J.W., Fensin, M.L., James, M.R., McKinney, G.W., Mashnik, S.G. and Waters, L.S. (2008) MCNPX User’s Manual. Version 2.6.0, National Laboratory, Los Alamos.

[38]   Matsuura, T., Egashira, Y., Nishio, T., Matsumoto, Y., Wada, M., Koike, S., Furusawa, Y., Kohno, R., Nishioka, S., Kameoka, S., Tsuchihara, K., Kawashima, M. and Ogino, T. (2010) Apparent Absence of a Proton Beam Dose Rate Effect and Possible Differences in RBE between Bragg Peak and Plateau. Medical Physics, 37, 5376-5381.

[39]   Farr, J.B., Mascia, A.E., His, W.C., Allgower, C.E., Jesseph, F., Schreuder, A.N., Wolanski, M., Nichiporov, D.F. and Anferov, V. (2008) Clinical Characterization of a Proton Beam Continuous Uniform Scanning System with Dose Layer Stacking. Medical Physics, 35, 4945-4954.

[40]   Carabe, A., Moteabbed, M., Depauw, N., Schuemann, J. and Paganetti, H. (2012) Range Uncertainty in Proton Therapy Due to Variable Biological Effectiveness. Physics in Medicine and Biology, 57, 1159-1172.

[41]   Carabe-Fernandez, A., Dale, R.G., Hopewell, J.W., Jones, B. and Paganetti, H. (2010) Fractionation Effects in Particle Radiotherapy: Implications for Hypo-Fractionation Regimes. Physics in Medicine and Biology, 55, 5685-5700.

[42]   Kramer, M. and Scholz, M. (2000) Treatment Planning for Heavy-Ion Radiotherapy: Calculation and Optimization of Biologically Effective Dose. Physics in Medicine and Biology, 45, 3319-3330.

[43]   Carlson, D.J., Stewart, R.D., Li, X.A., Jennings, K., Wang, J.Z. and Guerrero, M. (2004) Comparison of in Vitro and in Vivo Alpha/Beta Ratios for Prostate Cancer. Physics in Medicine and Biology, 49, 4477-4491.

[44]   Travis, E.L., Thames Jr., H.D., Tucker, S.L., Watkins, T.L. and Kiss, I. (1986) Protection of Mouse Jejunal Crypt Cells by WR-2721 after Small Doses of Radiation. International Journal of Radiation Oncology Biology Physics, 12, 807-814.

[45]   Girinsky, T., Lubin, R., Pignon, J.P., Chavaudra, N., Gazeau, J., Dubray, B., Cosset, J.M., Socie, G. and Fertil, B. (1993) Predictive Value of in Vitro Radiosensitivity Parameters in Head and Neck Cancers and Cervical Carcinomas: Preliminary Correlations with Local Control and Overall Survival. International Journal of Radiation Oncology Biology Physics, 25, 3-7.

[46]   Stuschke, M. and Thames, H.D. (1999) Fractionation Sensitivities and Dose-Control Relations of Head and Neck Carcinomas: Analysis of the Randomized Hyperfractionation Trials. Radiotherapy and Oncology, 51, 113-121.